Optimal regularity for phase transition problems with convection

  • Aram L. Karakhanyan

    Maxwell Institute for Mathematical Sciences and School of Mathematics, University of Edinburgh, King's Buildings, Mayfield Road, EH9 3JZ, Edinburgh, Scotland, UK

Abstract

In this paper we consider a steady state phase transition problem with given convection . We prove, among other things, that the weak solution is locally Lipschitz continuous provided that and is a harmonic function. Moreover, for continuous casting problem, i.e. when is constant vector, we show that Lipschitz free boundaries are regular surfaces.

Cite this article

Aram L. Karakhanyan, Optimal regularity for phase transition problems with convection. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 4, pp. 715–740

DOI 10.1016/J.ANIHPC.2014.03.003